The Effects of Fertilization and Deposition on Phosphorus Levels in the Plant-Soil System

By Lina Sorg

Phosphorous is essential to all life forms, sustaining plant and animal growth and maintaining the health of microbes that inhabit the soil. It circulates throughout the environment—moving through both water and land via marine and terrestrial organisms—in a biogeochemical cycle. Because phosphorous does not exist in a gaseous form, it is not transported via the atmosphere. It moves along a pathway, stopping to interact with biological systems along the way (see Figure 1). Therefore, the global phosphorus cycle is sometimes called a broken cycle.

Because the amount of phosphorous on land is constantly diminishing, an efficient local recycling element in the terrestrial ecosystem minimizes losses. During a minisymposium presentation at the 2021 SIAM Conference on Applications of Dynamical Systems, which is taking place virtually this week, Alina Dubovskaya of the University of Limerick modeled the way in which phosphorous is recycled in the plant-soil system. “We wanted to design a simple model to capture the main dynamic that we can analyze analytically,” she said. “We also wanted to include the spatial direction and see the vertical distribution of phosphorus in the soil in order to get some insights into the system.”

Dubovskaya designed a basic model to analyze the phosphorus recycling system (see Figure 2). Plants play an essential role in the system because they absorb phosphorous from the soil and move it above ground, where it becomes available to other organisms. When plants die, the phosphorous that is stored in their tissues accumulates on the soil surface in a layer of leaf litter. Microbes then transport the phosphorous back to the soil and process it so that it recirculates within the system and continues the cycle. However, a certain amount of phosphorus leaches from the groundwater into the underlying aquifer and leaves the system. Therefore, the model’s governing equations—which are essentially mass conservation equations—are written in terms of phosphorous content.

Dubovskaya used her model to generate a phosphorus soil profile. The vertical axis measures the soil depth (zero is the soil surface) and the horizontal axis tracks the concentration of phosphorus in the soil. The profile divides the soil into two zones. The upper zone contains plant roots that capture the phosphorus, move it above the ground, and circulate it through the system. The lower zone is comprised of subsoil; any phosphorus in this area is unreachable to plants, gradually moves into the underlying aquifer, and ultimately leaves the system. The soil profile indicates that the phosphorous concentration rapidly decreases within the root zone. In fact, most phosphorus is stored in the upper 20 centimeters of the soil — the area that is most vulnerable to erosion. The concentration of phosphorous below the root zone is actually quite small, indicating that the system is very efficient and losses via leaching are insignificant.

However, things changed when Dubovskaya added fertilization to the system (see Figure 3). Although fertilizer does not drastically alter the dynamics of the root zone, the concentration of phosphorus in the subsoil experiences a nearly twelvefold increase. This proliferation is concerning because the increased phosphorous flow eventually leaches out of the system. It enters rivers, lakes, and other bodies of water; causes an unusual growth of algae on the water surface that blocks sunlight; and essentially kills the ecosystem. The detrimental effects of fertilization are thus a substantial environmental concern for aquatic ecosystems.

Next, Dubovskaya removed some of the vegetation from the model and examined the resulting effect. She did so by accounting for the deposition rate, which is the percentage of vegetation that returns to the system. When the deposition rate is small—meaning that vegetation is routinely harvested—the concentration of phosphorus in the subsoil decreases and will eventually reach zero. “According to our model, it seems like the regular removal of vegetation is actually beneficial for phosphorous recycling,” Dubovskaya said. In this sense, phosphorus recycling seems to work effectively — everything that enters the soil is reused by the plants and keeps circulating. 

However, extreme harvesting rates change the system stability and leads to oscillations in vegetation. Such oscillations occur because plants grow at an almost exponential rate when large amounts of phosphorus are in the soil. As a result, they absorb increasingly more phosphorous, depleting the amount in the soil and causing other plants to die. Dead plants contribute to the leaf litter layer, which is ultimately returned back to the system; the amount of phosphorus in the soil increases again and the cycle repeats, just on a longer timescale.

Dubovskaya then explored the parameter space of the model’s two parameters: the fertilization and deposition rates. She conducted a stability analysis and assessed the resulting oscillations. “We want to produce a model that is suitable for explaining these oscillations,” she said. Dubovskaya utilized an asymptotic model and conducted an asymptotic analysis that captured the system’s dynamics, which are represented as delay differential equations. The boundary condition on the soil surface introduces the delay, which is caused by the resource regeneration time that is associated with the transfer of phosphorous in leaf litter to the soil where microbes can access it. Although the linear stability analysis nicely approximated the upper branch of Dubovskaya’s diagram, it did not successfully capture the lower portion. This is likely because the oscillations in vegetation span a very large period of 40 years, causing one to wonder whether they actually exist in reality. If they do, can researchers observe them? Dubovskaya plans to address these questions in future work.

Lina Sorg is the managing editor of SIAM News.